Question

In: Statistics and Probability

Suppose we examined samples of size n = 50 from the population of Basic Statistics classes...

Suppose we examined samples of size n = 50 from the population of Basic Statistics classes that I have taught at AU. Suppose that the sample mean is equal to 6.42 hours, and the population standard deviation is 6.72 hours.

a. Find a 95% confidence interval for the mean number of hours of television watched by this population of Basic Statistics students, using the information described above.

b. Does this confidence interval contain the population mean?

c. Suppose I gather 100 SRS of size 50, and I calculate 100 95% confidence intervals in the usual way. About how many of these would contain the population mean?

d. Find an 80% confidence interval for the mean number of hours of television watched by this population of Basic Statistics students.

e. Would it be good to use an 80% confidence interval? Why?

Solutions

Expert Solution


Related Solutions

Suppose samples of size 100 are drawn randomly from a population of size 1000 and the...
Suppose samples of size 100 are drawn randomly from a population of size 1000 and the population has a mean of 20 and a standard deviation of 5. What is the probability of observing a sample mean equal to or greater than 21?
Suppose we have a random sample of size 50 from a N(μ,σ2) PDF. We wish to...
Suppose we have a random sample of size 50 from a N(μ,σ2) PDF. We wish to test H0: μ=10 versus H1: μ=10. The sample moments are x ̄ = 13.4508 and s2 = 65.8016. (a) Find the critical region C and test the null hypothesis at the 5% level. What is your decision? (b) What is the p-value for your decision? (c) What is a 95% confidence interval for μ?
Random samples of size n = 90 were selected from a binomial population with p =...
Random samples of size n = 90 were selected from a binomial population with p = 0.8. Use the normal distribution to approximate the following probability. (Round your answer to four decimal places.) P(p̂ > 0.78) =
Random samples of size n = 60 were selected from a binomial population with p =...
Random samples of size n = 60 were selected from a binomial population with p = 0.2. Use the normal distribution to approximate the following probabilities. (Round your answers to four decimal places.) (a)     P(p̂ ≤ 0.22) = (b)     P(0.18 ≤ p̂ ≤ 0.22) =
A random sample of size n = 50 is taken from a population with mean μ...
A random sample of size n = 50 is taken from a population with mean μ = −9.5 and standard deviation σ = 2. [You may find it useful to reference the z table.] a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. (Negative values should be indicated by a minus sign. Round "expected value" to 1 decimal place and "standard deviation" to 4 decimal places.) Expected Value= Standard Error= b. What...
Suppose a simple random sample of size n=75 is obtained from a population whose size is...
Suppose a simple random sample of size n=75 is obtained from a population whose size is N= 30,000 and whose population proportion with a specified characteristic is p= 0.4 . A) Determine the standard deviation of the sampling distribution of p hat (Round to 6 decimals) B) What is the probability of obtaining x=33 or more individuals with the​ characteristic? That​ is, what is ​P(p ≥0.44​)? (Round to 4 decimals)
Suppose a simple random sample of size n=1000 is obtained from a population whose size is...
Suppose a simple random sample of size n=1000 is obtained from a population whose size is N=2,000,000 and whose population proportion with a specified characteristic is p = 0.22 a. What is the probability of obtaining x=250 or more individuals with the​ characteristic?
Suppose a simple random sample of size n=75 is obtained from a population whose size is...
Suppose a simple random sample of size n=75 is obtained from a population whose size is N=15,000 and whose population proportion with a specified characteristic is p=0.8. a) Determine the mean of the sampling distribution of p with caret. Determine the standard deviation of the sampling distribution of p with caret. b) What is the probability of obtaining x=66 or more individuals with the​ characteristic? That​ is, what is ​P(p with caret greater than or equals 0.88)? What is the...
Suppose a simple random sample of size n= 1000 is obtained from a population whose size...
Suppose a simple random sample of size n= 1000 is obtained from a population whose size is N=2,000,000 and whose population proportion with a specified characteristic is p= 0.65. (a) Describe the sampling distribution of (b) What is the probability of obtaining x= 690 or more individuals with the​ characteristic? (c) What is the probability of obtaining x = 620 or fewer individuals with the​ characteristic?
Suppose a simple random sample of size n=200 is obtained from a population whose size is...
Suppose a simple random sample of size n=200 is obtained from a population whose size is Upper N= 20,000 and whose population proportion with a specified characteristic is p equals 0.6 .p=0.6. Complete parts ​(a) through​ (c) below. (a) Determine the standard deviation (b) What is the probability of obtaining x=124 or more individuals with the​ characteristic? That​ is, what is ​P(p≥0.62)? (c) What is the probability of obtaining x=106 or fewer individuals with the​ characteristic? That​ is, what is...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT